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Gambler's fallacy, hot hand belief, and the time of patterns

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  • Yanlong Sun
  • Hongbin Wang

Abstract

The gambler's fallacy and the hot hand belief have been classified as two exemplars of human misperceptions of random sequential events. This article examines the times of pattern occurrences where a fair or biased coin is tossed repeatedly. We demonstrate that, due to different pattern composition, two different statistics (mean time and waiting time) can arise from the same independent Bernoulli trials. When the coin is fair, the mean time is equal for all patterns of the same length but the waiting time is the longest for streak patterns. When the coin is biased, both mean time and waiting time change more rapidly with the probability of heads for a streak pattern than for a non-streak pattern. These facts might provide a new insight for understanding why people view streak patterns as rare and remarkable. The statistics of waiting time may not justify the prediction by the gambler's fallacy, but paying attention to streaks in the hot hand belief appears to be meaningful in detecting the changes in the underlying process.

Suggested Citation

  • Yanlong Sun & Hongbin Wang, 2010. "Gambler's fallacy, hot hand belief, and the time of patterns," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 5(2), pages 124-132, April.
  • Handle: RePEc:jdm:journl:v:5:y:2010:i:2:p:124-132
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    References listed on IDEAS

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    1. Matthew Rabin & Dimitri Vayanos, 2010. "The Gambler's and Hot-Hand Fallacies: Theory and Applications," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 730-778.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Rachel Croson & James Sundali, 2005. "The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos," Journal of Risk and Uncertainty, Springer, vol. 30(3), pages 195-209, May.
    4. James Sundali & Rachel Croson, 2006. "Biases in casino betting: The hot hand and the gambler's fallacy," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 1, pages 1-12, July.
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    Cited by:

    1. Andrey Kudryavtsev & Gil Cohen & Shlomit Hon-Snir, 2013. "“Rational” or “Intuitive”: Are Behavioral Biases Correlated Across Stock Market Investors?," Contemporary Economics, University of Finance and Management in Warsaw, vol. 7(2), June.
    2. Joshua B. Miller & Adam Sanjurjo, 2014. "A Cold Shower for the Hot Hand Fallacy," Working Papers 518, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. William J. Matthews, 2010. "The gambler's fallacy in retrospect: A supplementary comment on Oppenheimer and Monin (2009)," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 5(2), pages 133-137, April.
    4. Nunnari, Salvatore & Zapal, Jan, 2016. "Gambler's fallacy and imperfect best response in legislative bargaining," Games and Economic Behavior, Elsevier, vol. 99(C), pages 275-294.

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